Former Secretary of State Hillary Rodham Clinton addresses the World Bank Group's report 'Voice and Agency: Empowering Women and Girls for Shared Prosperity' at World Bank headquarters in Washington, Wednesday, May 14, 2014.

Cliff Owen/AP

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Washington — A new poll shows Hillary Rodham Clinton well in front of potential GOP presidential rivals in Ohio, one of the biggest and most important swing states in national elections.

The Quinnipiac University survey puts former Secretary of State Clinton ahead of former Florida Gov. Jeb Bush by 48 to 39 percent. She leads Sen. Marco Rubio of Florida by 47 to 40 percent and Sen. Rand Paul of Kentucky by 49 to 41 percent. She’s ahead of Sen. Ted Cruz of Texas by 51 to 37 percent.

Clinton’s closest competitor in the Buckeye State seems to be Ohio’s GOP Gov. John Kasich, who’s been mentioned as a dark-horse presidential candidate by some party bigwigs. Clinton leads Kasich by five percentage points, 47 to 42.

“Gov. John Kasich runs best against Secretary Hillary Clinton for 2016 among eight Republican candidates, although her lead over most of them has dropped considerably since Quinnipiac University surveyed Ohio voters in February,” says Peter A. Brown, assistant director of the Quinnipiac University Poll.

On the surface, this poll looks OK for Clinton. But if we were one of her pollsters, prepping for the possibility of a presidential bid, there’s stuff here we’d be worried about.

Not that we’d be too concerned: It’s so early there is little connection between such polls and actual electoral results more than two years hence. But there are trends we’d be keeping an eye on.

First, as Mr. Brown noted, this poll shows the state tightening up. Clinton has lost between three and five points on her various rivals since Quinnipiac last surveyed Ohio in February.

Look deeper in the data, and you see that much of this decline appears to have come from Republicans who previously supported Clinton drifting back to their preferred party. But Clinton seems to have lost some support among men, too. For instance, in February 45 percent of male voters said they’d vote for Clinton in a notional race against Mr. Bush. In May that percentage dropped to 40 percent.

That could just be margin-of-error stuff, but we’d be watching that if we were on Clinton’s payroll.

Second, the Quinnipiac survey isn’t good for President Obama. It puts his favorable rating in the state underwater, with 39 percent of Ohio voters saying they approve of the job he’s doing and 58 percent saying they disapprove.

That’s about five points worse than he’s doing in the nation as a whole, according to the RealClearPolitics rolling average of major surveys. That might indicate Democrats are losing ground in a key state.

“Such a consistently low rating can’t be helpful to the Democratic ticket,” says Quinnipiac’s Brown, referring to upcoming midterms in which Ohio will elect a governor, among other officials.

Hillaryland also might just chew on the fact that they know these numbers are going to get worse, and she’ll face “Slipping in Ohio” headlines. They’ll slide because almost all her currently high ratings are partly due to her being one of the most well-known women in the world. Polls show that almost every time a very famous person actually declares for president, their approval ratings begin to slip, wrote Aaron Blake, Washington Post political expert, earlier this week.

“Indeed, the idea that Clinton will continue to post a big lead on whomever the GOP puts up is pretty far-fetched,” Mr. Blake writes.